China's biggest contributions to the Bay Area economy come from students, tourists and real estate investment. Other sectors are doing OK, but a slowing China economy means ties aren't growing as quickly as some anticipated.

Those are the takeaways from a study published Friday by the Bay Area Council Economic Instituteon the economic links connecting San Francisco and the Silicon Valley with the global superpower.

Which means California's new trade representative in China has her work cut out for her. "It's deal by deal, visit by visit," said Diane Long, before she left for Shanghai last month.

Long, formerly a managing director at Xanadu Enterprise, an international business consultancy in Shanghai, knows much is expected - California's previous taxpayer-funded trade office (hers is under the Bay Area Council's roof), didn't work out too well and was shut down in 2003 by then-Gov. Arnold Schwarzenegger.

The job involves lots of travel and meet-and-greets, during which Long hopes to advocate for the state's low-hanging fruit, like movies, tech, and food and agriculture.

Makes sense, considering China's ongoing problems with food safety.

"The food chain is a leading edge opportunity," she said.

Tourists, students

Chinese students and tourists, meanwhile, are flying here in increasing numbers. Science, technology and math grads continue to flock to Stanford and UC Berkeley, although more are returning home sooner after getting their advanced degrees. Reported endowments from Chinese donors to Berkeley and Stanford total more than $150 million.

There's also been a surge of Chinese undergraduates, which couldn't come at a better time for cash-strapped state schools. An estimated 7,000 Chinese students from "Greater" China (including Hong Kong and Taiwan) studied here in 2012, bringing close to $220 million in state coffers, says the report.

One problem: "Many undergraduates show up unprepared, scholastically and in English language proficiency."

Tourism continues to hum, with over 300,000 tourists from the mainland, Taiwan and Hong Kong in San Francisco in 2011, according to SFTravel. But the style of travel is changing.

"The profile of Chinese tourism is shifting from lower-end packaged tours to more and wealthier Chinese traveling as individuals," the study says.

Then there's real estate.

"That's the big story," said Sean Randolph, president of the institute. "Chinese investors are scouting around the Bay Area as we speak."

It's difficult to put a figure on how big, with an untold number of Chinese buyers snatching up pieds-a-terre, snagging homes for their college-age kids, and putting cash behind development projects. According to the report, Chinese financial investment in the Bay Area stood at $495 million in 2011 - 7 percent of all foreign private investment in the region - but counting in real estate, the number could be in the billions, said Cooper.

"Most real estate investment coming out of China you don't read about," he said, with knowing nods from the audience.

Breaking into China

All in all, a reasonably satisfactory report. Close to 200 branches of Greater Chinese companies in the Bay Area, including 51 from the mainland. Tech companies like Huawei and China Mobile have R&D labs here. Baidu, the biggest search engine on the mainland, is opening an artificial intelligence lab - the Institute of Deep Learning - in Cupertino.

But it's still hard for California companies to establish themselves in China. Banks face currency restrictions trading in yuan, and tech brands encounter a myriad of hurdles.

There are thorny issues like intellectual property theft, technology transfer and cybersecurity, and the Chinese government's increasingly harsh crackdown on its own citizens. Those and other limitations stand in the way of some U.S. innovators and social networks, like Facebook and Twitter, which remain shut out. China's e-commerce company, Alibaba - 24 percent owned by Yahoo - is phasing out all of Yahoo's brands there.

Despite the challenges, some local businesses have recently broken through. Tesla is gearing up for a China launch of its electric cars, and Apple's iPhones are sold there via China Mobile. Google's Android operating system powers 90 percent of Chinese smartphones.

"While China will remain a sometimes controversial topic in Washington, states, regions and private companies tend to see China more pragmatically," the report said.

Best bet, as Long reminded me: Remember the Chinese saying about "crossing the river by feeling for stones."